Azarenka took 63 minutes to crush Paszek and will meet Roberta Vinci of Italy next after her 6-3 6-1 win over France's Pauline Parmentier.
Earlier, former French Open champion Li Na shrugged off a nasty cough to beat Russia's Anastasia Pavlyuchenkova 7-5 4-6 6-2 and reach the last 16.
Li's appearance in Tokyo was a relief for organisers after China withdrew its badminton players from last week's Japan Open amid tensions over disputed islands in the East China Sea.
Playing on an outside court, Li lacked sharpness after a whirlwind book-signing tour in China following the release of her autobiography.
However, the 30-year-old saved her best for the big points, putting the match away by smashing a cross-court backhand into the corner after two hours, 37 minutes.
Next up for Li is Caroline Wozniacki after the Dane defeated Slovakian Daniela Hantuchova 7-6 6-1.
Former Wimbledon champion Petra Kvitova was bundled out in the first upset of the WTA premier five event, suffering a 6-4 6-4 defeat by Croatia's Petra Martic.
The fourth seed squandered numerous opportunities against her 72nd-ranked opponent, who closed out the match with a fierce serve which almost knocked the Czech over.
"That was the biggest win of my career so far," smiled Martic. "The last five or six days have been really weird. I've played bad in practice and just couldn't do anything."
Martic next faces Russia's Nadia Petrova after the 17th seed beat Romania's Simona Halep 7-6 6-0.
Nine of the world's top 10 women are appearing in the hardcourt tournament, US Open champion Serena Williams the only player absent.
Germany's Angelique Kerber made short work of Japanese wildcard Ayumi Morita, the fifth seed comfortably winning 6-3 6-4 to reach the third round.
Kerber will now face Urszula Radwanska following her 3-6 6-4 6-2 win over Ana Ivanovic.
Urszula's elder sister Agnieszka Radwanska also defeated Serbian opposition to progress, overcoming Jelena Jankovic 6-2 7-5 to set up a round of 16 encounter with American Jamie Hampton, victor over Estona's Kaia Kanepi 5-7 6-2 6-3.
Sam Stosur will meet Dominika Cibulkova after the Australian saw off Italy's Francesca Schiavone 4-6 7-6 6-4 and the Slovak downed Jie Zheng 6-0 6-3.
Sixth seed Sara Errani of Italy beat Sweden's Johanna Larsson 6-3 7-6 and next faces Frenchwoman Marion Bartoli after the ninth seed's 6-2 7-5 win over German Julia Goerges.
Maria Sharapova had to dig deep to overcome Britain's Heather Watson in three sets, eventually winning 6-7 6-3 6-4.
- Anastasia Pavlyuchenkova
- Roberta Vinci
- Petra Martic